Smagorinsky Model Research Articles

Subgrid-scale model considering the inverse energy cascade using an artificial neural network

For the closure of the subgrid-scale (SGS) stress tensor, an artificial neural network (ANN)-based SGS model that takes account of the inverse energy cascade in isotropic turbulence is developed. The data required for training this ANN-based SGS model are provided by direct numerical simulation of isotropic turbulence with an inverse energy cascade. Two input features, the root mean square of the rate-of-strain tensor and the product of the eigenvalues of the rate-of-strain tensor, are employed to characterize the inverse energy cascade. An a priori test reveals that the ANN-based model adequately predicts the SGS stress tensor in the backward energy transfer process, and the predictive capability of the gradient model is found to be slightly poorer than that of the ANN-based model, while that of the Smagorinsky model is not satisfactory. In comparison with the gradient model, the ANN-based model even predicts a few backward energy transfer events in the stage of excessive energy dissipation. In addition, the off-diagonal component of the SGS stress tensor, rather than the diagonal component, may be intimately associated with the inverse energy cascade. The ANN-based SGS model presented here is expected to provide inspiration for future investigations of the construction of SGS models that take account of the inverse energy cascade.

Large Eddy Simulation of an impinging Jet for Cooling of Blades

Abstract The impinging jet shows extremely high performance in local blade cooling and has been widely applied. In this study, high precision Large Eddy Simulation (LES) was employed to simulate compressible fully turbulent impinging jet under specific conditions, using three subgrid-scale (SGS) models - the Smagorinsky model (SM), the Coherent-structure Smagorinsky Model (CSM), and the Selective Mixed Scale Model (SMSM). The predictive accuracy and computational efficiency of the three SGS models were evaluated. Compared with existing DNS and experimental results, the results indicate that there is no significant difference among the three models in computational efficiency. However, subgrid models have a crucial impact on heat transfer. The SMSM model, which utilizes small-scale turbulence information, can better simulate the heat transfer in the impingement region compared with the SM model and the CSM model.

A Dynamic Smagorinsky Model for Horizontal Turbulence Parameterization in Tropical Cyclone Simulation

AbstractThe horizontal turbulence parameterization is vital for the intensity and structure forecasting of tropical cyclone (TC) in numerical weather prediction (NWP) models. The default two‐dimensional (2D) standard Smagorinsky model with a single universal constant in Weather and Research Forecasting (WRF) model has been proven to be over dissipative for TC, leading to underprediction of TC intensity. This study provides the first attempt to implement the physically based 2D dynamic Smagorinsky model (DSM) for horizontal turbulence parameterization in WRF model for TC forecasts. The DSM dynamically computes the Smagorinsky coefficient as a function of the resolved flow during the simulation, avoiding the need to prescribe the coefficient a prior. The test results of the DSM in a TC NWP model show that the DSM can significantly improve the wind intensity forecasts compared to the standard Smagorinsky model.

A novel subgrid-scale stress model considering the influence of combustion on turbulence: A priori and a posteriori assessment

Most classical turbulence models were proposed and developed based on non-reacting flows without considering the effects of combustion on turbulence. The flow structure in turbulent combustion is more complex, creating challenges to the applicability of traditional turbulence models. Given this, a novel flame surface and k-equation-based gradient model (FKGM) considering combustion effects is proposed for the modeling of the subgrid-scale (SGS) stress in large eddy simulation (LES). The SGS stress is calculated based on the SGS kinetic energy (kSGS) and normalized velocity gradient. The velocity gradient incorporates first-order gradients at multiple stencil locations and considers the anisotropy of the stress near the flame surface. The FKGM model is first validated by the a priori analysis based on the direct numerical simulation (DNS) database of a premixed swirling flame. The closure terms of the kSGS equation are well validated, and the predicted SGS stress using the FKGM model achieves good agreement with the filtered DNS results. In the a posteriori LES study, the FKGM model demonstrates better performance compared with the traditional dynamic Smagorinsky model and velocity gradient model, providing more accurate predictions for mean and fluctuation velocities. The error analysis for SGS kinetic energy is further conducted by comparing the LES results with the DNS data, and the results indicate that the underestimation of the generation term of the kSGS equation is the main source of error.

Dynamics of turbulent natural convection in a cubic cavity with centrally placed partially heated inner obstacle

Natural convection in a cavity with a partially heated obstacle at the center at the Rayleigh number Ra=1.46×109 is investigated using large eddy simulation (LES). The standard and dynamic Smagorinsky models, as well as the wall-adapting local eddy-viscosity model, are used for the subgrid scales, and the flow statistics are compared with recent experiments. The LES results obtained with different meshes show overall good agreement with the experiments as concerns the flow and heat transfer. Simulation with a non-ideal wall at the adiabatic side of the obstacle is also performed to explain the residual discrepancies observed in the unheated channel. Additional simulations performed with periodic conditions in the spanwise direction are very different from the full three-dimensional (3D) simulations, which demonstrate the significance of 3D effects in the cavity. In particular, periodic simulations show Tollmien–Schlichting kind waves in the transitional region, while the 3D cavity shows an early cross-flow transition to turbulence.

Grey‐zone simulations of shallow‐to‐deep convection transition using dynamic subgrid‐scale turbulence models

AbstractWe examine the ability of two dynamic turbulence closure models to simulate the diurnal development of convection and the transition from dry to shallow cumuli and then to deep convection. The dynamic models are compared with the conventional Smagorinsky scheme at a range of cloud‐resolving and grey‐zone resolutions. The dynamic schemes include the Lagrangian‐averaged, scale‐dependent dynamic Smagorinsky model and a Lagrangian‐averaged, dynamic mixed model. The conventional Smagorinsky model fails to reproduce the shallow convection stage beyond the large‐eddy simulation regime, continuously building up the convective available potential energy that eventually leads to an unrealistic deep convection phase. The dynamic Smagorinsky model significantly improves the representation of shallow and deep convection; however, it exhibits issues similar to the conventional scheme at coarser resolutions. In contrast, the dynamic mixed model closely follows the large‐eddy simulation results across the range of sub‐kilometre simulations. This is achieved by the combined effect of an adaptive length scale and the inclusion of the Leonard terms, which can produce counter‐gradient fluxes through the backscatter of energy from the subgrid to the resolved scales and enable appropriate non‐local contributions. A further sensitivity test on the inclusion of the Leonard terms on all hydrometeor fluxes reveals the strong interaction between turbulent transport and microphysics and the possible need for further optimisation of the dynamic mixed model coefficients together with the microphysical representation.

Prediction of heat exchanger efficiency using laminar heat transfer in swirling flow of radiated graphene oxide with nano fluid additives using machine learning technique

Nanotechnology has recently led to new possibilities for enhancing heat transfer in heat exchangers. The remarkable thermal characteristics of graphene oxide (GO)-based nanofluids with nanoscale additions have garnered significant attention in particular. When nanofluids and intricate flow patterns are involved, traditional analytical models frequently fail to appropriately forecast the efficiency of heat exchangers. Analyzed the phenomenon of laminar heat transfer in a heat exchanger that has a swirling flow of fluid dynamics, and pressure drop, and predicted the condensation heat transfer coefficient (HTC) of LHT. The functionalized radiated GO was chosen as nanomaterials in the present for the Pre-processing of Data Methods for managing outliers by machine learning (ML) models, like the CLAHE algorithm. The logarithmic mean temperature difference (LMTD) can be used to determine the temperature driving power for heat transfer within a heat exchanger. The Dynamic Smagorinsky Model (DSLM) and Wall-Adapting Local Eddy-viscosity (WALE) Model are turbulence models primarily designed for capturing turbulent behavior in fluid flows. The Kern technique and Hagen–Poiseuille equation are used for the pressure drop and pumping power needed in a shell and tube in laminar flow through a microtube based on Levenberg–Marquardt and Momentum Algorithm to predict Nusselt number and pressure drop in heat exchangers. The prediction sensitivity of the HTC by an LHT-trained ML model is used to evaluate the performance. The ML methods may be effectively used to forecast and maximize heat exchanger performance in the setting of laminar heat transfer in radiated GO nanofluid swirling flows. The accuracy score of 99%, demonstrating its exceptional predictive capabilities and results has great potential to improve energy efficiency, save operating costs, and advance sustainable practices in various industrial applications.

High-fidelity simulations of boundary layer transition on an underwater axisymmetric body with stability theory

During the cruise status of an underwater high-speed vehicle, the flow around the vehicle's head typically transitions from a laminar to a turbulent state, triggering flow noise that can interfere with the normal operation of sonar. In order to accurately investigate this flow noise through numerical simulation, a high-fidelity turbulent flow field solution is essential. Common traditional turbulence numerical simulation methods, such as unsteady Reynolds-averaged simulation and large eddy simulation (LES), struggle to capture high-frequency turbulent fluctuations accurately due to their inability to directly resolve small-scale eddy structures, which results in compromising the simulation accuracy of high-frequency flow noise. To address this issue, this paper employs direct numerical simulation (DNS) to achieve high-fidelity resolution of the turbulent flow field, thereby enabling a more accurate assessment of flow noise distribution on the vehicle's surface. Meanwhile, considering significant computational resources required to solve the entire flow field in an underwater high Reynolds number environment, this study also incorporates the fixed transition modeling method and stability theory to confine the DNS computational domain to the vicinity of the transitional zone to improve simulation efficiency. Comparative analysis of flow noise monitoring results in the laminar, transitional, and turbulent zones revealed that the flow noise source in the laminar zone exhibits the lowest amplitude across all frequencies, while the flow noise source in the transitional zone features the highest amplitude, approximately 10 dB higher than that in the turbulent zone. Moreover, significant amplitudes in high-frequency components (above 30 kHz) are detected in both the transition and turbulent zones. Additionally, this study employs LES with the Smagorinsky model to simulate the flow field within the same computational domain as DNS, demonstrating the limitations of the Smagorinsky model-based LES in capturing high-frequency flow noise.

Three-dimensional large eddy simulation urban neighborhood model with updated building drag coefficient and universal multiscale Smagorinsky model

Three-dimensional large eddy simulation urban neighborhood model with updated building drag coefficient and universal multiscale Smagorinsky model

Evaluation of flow and flame characteristics of turbulent bluff-body CH4-H2 flame using LES-FPV approach

ABSTRACT This study investigated the flow and flame structure of a bluff-body stabilised CH4-H2 flame using the large eddy simulation (LES) and the flamelet progress variable (FPV) model. The performance of three subgrid-scale (SGS) LES models, i.e. the standard Smagorinsky model (SSM), the wall-adapting local eddy viscosity (WALE) model, and the dynamic Smagorinsky model (DSM) in predicting turbulent and reactive flow characteristics was assessed. Parameters, namely y+ , Pope index (M), vorticity field, and resolved turbulent kinetic energy (kt ), were analysed to determine the predictive capability of the three models. The results demonstrated that DSM and WALE successfully resolved 80% of kt for chosen grid configurations, whereas SSM exhibited discrepancies. The overall trends captured by all three models matched well with the experimental trend with DSM and WALE outperforming SSM in predicting reacting flow fields in the recirculation zone, while SSM produced better predictions in the regions away from the recirculating zone.

Large-Eddy Simulations with remeshed Vortex methods: An assessment and calibration of subgrid-scale models

This study assesses various subgrid-scale models within the framework of Large Eddy Simulation (LES) using a remeshed Vortex method (RVM). RVM is a semi-Lagrangian method discretizing the vorticity-velocity Navier–Stokes equations that has proven to be a stable and less dissipative alternative to more classical Eulerian methods. The subgrid-scale models are first tested on the well-known Taylor–Green Vortex case at Re=5000. Notably, the Variational Multiscale (VMS) variant of the Smagorinsky model and the Spectral Vanishing Viscosity (SVV) approaches emerge as the best-suited to the RVM, as they add diffusion to only the smallest resolved vorticity scales. Then, a stochastic uncertainty quantification analysis is conducted for both selected models, and the model coefficients are calibrated against direct numerical simulation. These coefficients are then applied to additional cases (different regimes, grid resolutions and test cases), showing the robustness of the calibration within the RVM-LES framework.

Modelling urban canopy with object-based porosity model

We present a novel approach to modelling urban canopies based on the porosity model. The impact of objects in the canopy layer is implicitly accounted for by applying a high-value drag force in the parts of the canopy layer that objects would occupy. This effectively halts fluid flow in the defined space of the objects, mimicking the impact of solid objects in the canopy layer. The model addresses two common issues in urban canopy modelling: the definition of the drag coefficient and the loss of canopy morphology, which significantly affect flow and turbulence fields. The model is assessed for three cases: two idealised urban-like canopies with realistic urban flow conditions and one benchmark case based on the measurements of Hilderman and Chong (2007). The benchmark results, where the explicitly modelled objects are reduced from 109 to 9, show that the new model exhibits a level of accuracy similar to explicit modelling. We also computed the commonly used zone-based porosity and roughness models for the two idealised urban-like canopies. The new model produced results comparable to the results of explicit modelling and superior to those of the alternative approaches. All cases were computed in unsteady mode using a hybrid RANS/LES model based on elliptic-relaxation eddy-viscosity RANS and the dynamic Smagorinsky model. The simulations were performed using the open-source computational fluid dynamics code T-Flows, available on Github.

Turbulence modeling of stratified turbulence using a constrained artificial neural network

For large eddy simulations (LES) of stratified turbulence in the strongly stratified regime, an artificial neural network (ANN) with five hidden layers is used to construct a sub-grid scale (SGS) model. The ANN is assessed by comparing it to the Smagorinsky model, the dynamic Smagorinsky model, the gradient model, and filtered direct numerical simulation data. In the a priori test, the SGS model using ANN performed better than the Smagorinsky model and the gradient model in terms of the correlation coefficient and relative error of the energy transfer rate. However, the ANN does not provide sufficient energy dissipation when it is applied to LES with a larger filter width because it overpredicts backscatter. To address this problem, we also trained a constrained ANN using a custom loss function that penalizes excessive backscatter. It is shown that the constrained ANN successfully predicts less backscatter, maintaining the high correlation coefficient without ad hoc clipping. These results show that ANN is a promising tool for realizing a highly accurate and stable SGS model for stratified turbulence.

Large-eddy simulation of wind pressures on elevated low-rise buildings

Residential buildings in coastal communities are often elevated to mitigate flooding and wave-surge impacts. However, the elevations change the local wind field characteristics and may increase the aerodynamic pressure on buildings. Post-event reconnaissance showed that elevated buildings experienced severe structural damage to the roofs, walls, and floors during major hurricanes. Currently, our understanding of aerodynamic pressure on elevated houses is limited. In this paper, a large eddy simulation (LES)-based method is developed to better understand the wind effects on elevated buildings. The inflow generation method, discretizing and synthesizing random flow generation, is adopted to generate inflow boundary conditions satisfying the target spectrum. Two sub-grid scale models, the Smagorinsky and wall-adapted local eddy-viscosity models, are employed to represent the unresolved small-scale eddies. It is found that the eddy structure sizes can strongly affect the pressure fluctuations at the eddy separation zones. The present study advances the understanding of aerodynamics on elevated buildings and provides a reference for future LES-based research on wind effect modeling.

An Implicit Factorized Transformer with Applications to Fast Prediction of Three-dimensional Turbulence

Transformer has achieved remarkable results in various fields, including its application in modeling dynamic systems governed by partial differential equations. However, transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence. In this paper, we propose an implicit factorized transformer (IFactFormer) model, which enables stable training at greater depths through implicit iteration over factorized attention. IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence (HIT), and is shown to be more accurate than the FactFormer, Fourier neural operator (FNO), and dynamic Smagorinsky model (DSM) in the prediction of the velocity spectra, probability density functions of velocity increments and vorticity, temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity. IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT. Furthermore, IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.

A fully-resolved LBM-LES-DEM numerical scheme for adhesive and cohesive particle-laden turbulent flows in three dimensions

Adhesive and cohesive particle-laden turbulent flows play a crucial role in numerous natural and industrial processes. Herein, a fully-resolved LBM-LES-DEM numerical scheme is developed for a better understanding of these flows in three dimensions. This numerical scheme is four-way coupling, where the adhesive and cohesive forces, such as van der Waals force, capillary force and viscous force, are embedded into DEM to simulate adhesive and cohesive particle-particle interactions, and the MRT-D3Q19 LBM is combined with LES based on the Smagorinsky model to simulate turbulent fluid flows, and the fluid-particle interactions are solved by momentum exchange method. Several benchmarks, such as 3D duct flow, single particle settling, and DKT processes, are validated, and the dynamics of particle pair in turbulent structures are further discussed. All the results indicate that this numerical scheme provides a promising method for the simulation of adhesive and cohesive particle-laden turbulent flows.

Large eddy simulation of a turbulent channel flow using dynamic Smagorinsky subgrid scale model and differential equation wall model

A large eddy simulation (LES) is conducted in a plane channel flow which is turbulent. For understanding the mechanism of the turbulent motion more efficiently, the present study is an attempt to conduct the LES using a Dynamic Smagorinsky Model (DSM) and a Differential Equation Wall Model (DEWM). DSM is a subgrid-scale model and DEWM is for approximating the near wall layer. The simulation is performed in a domain of 2 π δ × 2 δ × π δwhich is discretized by 32 × 20 × 32grid points where δ is the channel half width. The discretization techniques have been used in the simulation, are the 3rd order low storage R-K method in time and 2nd order finite difference formulation in space. To assess the performance of the LES with DSM and DEWM, the simulation results are compared with direct numerical simulation (DNS) data and LES data using Standard Smagorinsky Model (SSM). Comparing the results in the essential turbulence statistical field it has been found that DSM performs better than SSM in most of the cases and shows better agreement with the DNS results. Flow structures in the turbulent flow field are compared in isosurfaces and contour plots, and found that tube-like vortical structures are randomly distributed over the entire flow field, and the number of the vortical structures are more for the DSM case than that of SSM.

One- and two-level Arrow–Hurwicz-type iterative algorithms for the stationary Smagorinsky model

In this article, based on finite element discretization, we propose one- and two-level Arrow–Hurwicz-type iterative algorithms for solving the steady-state Smagorinsky equations. The two-level Arrow–Hurwicz-type iterative algorithm involves solving a linearization Smagorinsky problem by the Arrow–Hurwicz-type iteration on a coarse mesh with mesh size H, and one Oseen-type linear problem on a fine mesh with mesh size h. Stability analysis and error estimation are provided. Compared with the classical Arrow–Hurwicz algorithm, the proposed algorithms have less constriction concerning parameter. Finally, we test some numerical experiments to illustrate the effectiveness of the proposed algorithms.

A mathematical‐boundary‐recognition domain‐decomposition Lattice Boltzmann method combined with large eddy simulation applied to airfoil aeroacoustics simulation

AbstractBeing a direct computational aeroacoustics method, Lattice Boltzmann method (LBM) has great potential and broad application perspective in the field of numerical simulation of aerodynamic noise due to its low dispersion and low dissipation. A series of numerical algorithms and the related improvements based on the standard LBM method are proposed and developed in this paper to adapt to the airfoil noise calculation with complex grid at middle‐high Reynolds number. First, a new mathematical‐boundary‐recognition algorithm based on Green's formula is proposed to deal with complex curved geometric models, which is validated by three‐element airfoil 30P30N benchmark. Then, in order to reduce grid redundancy and improve computing efficiency, the grid refinement technique of domain decomposition model (DDM) is adopted and also improved, which is verified by calculating the flow and sound fields around 2D and 3D cylinders at Reynolds number equal to 90,000. Finally, three different LES turbulence models are combined with the standard MRT‐LBM method, where different finite difference schemes are used to solve Reynolds stress tensor which is different from the traditional one. Through the direct acoustic numerical simulation of NACA0012 airfoil at Reynolds number equal to 200,000, the effects of Smagorinsky models and Wall‐adapting local eddy‐viscosity (WALE) model on aerodynamic noise prediction are compared and analyzed. Overall, the proposed methodology is shown to be appropriate for predicting the aerodynamic noise at low Mach number and can successfully simulate the generation and propagation of far field acoustics.

Large eddy simulation of flow over a circular cylinder with a neural-network-based subgrid-scale model

A neural-network-based large eddy simulation is performed for flow over a circular cylinder. To predict the subgrid-scale (SGS) stresses, we train two fully connected neural network (FCNN) architectures with and without fusing information from two separate single-frame networks (FU and nFU, respectively), where the input variable is either the strain rate (SR) or the velocity gradient (VG). As the input variables, only the grid-filtered variables are considered for the SGS models of G-SR and G-VG, and both the grid- and test-filtered variables are considered for the SGS models of T-SR and T-VG. The training data are the filtered direct numerical simulation (fDNS) data at $Re_d=3900$ based on the free-stream velocity and cylinder diameter. Using the same grid resolution as that of the training data, the performances of G-SR and G-VG (grid-filtered inputs) and T-SR-FU and T-VG-FU (grid- and test-filtered inputs with fusion) are better than those of the dynamic Smagorinsky model and T-SR-nFU and T-VG-nFU (grid- and test-filtered inputs without fusion). These FCNN-based SGS models are applied to untrained flows having different grid resolutions from that of training data. Although the performances of G-SR and G-VG are degraded, T-SR-FU and T-VG-FU still provide good performances. Finally, T-SR-FU and T-VG-FU trained at $Re_d = 3900$ are applied to higher-Reynolds-number flows ( $Re_d = 5000$ and 10 000) and their results are also in good agreements with those of fDNS and previous experiment, indicating that adding the test-filtered variables and fusion increases the prediction capability even for untrained Reynolds number flows.